In this paper we give a new proof of Richardson's theorem [31]: a global function G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] of a cellular automaton [MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is injective if and only if the inverse of G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is a global function of a cellular automaton. Moreover, we show a way how to construct the inverse cellular automaton using the method of feasible interpolation from [20]. We also solve two problems regarding complexity of cellular (...) automata formulated by Durand [12]. (shrink)

The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. The principle is important as the basis for ecological theory. On a relatively simple model we show a mechanism of indefinite coexistence of complete competitors which violates the known formulations of the competitive exclusion principle. This mechanism is based on timely recovery of limiting resources and their spatio-temporal allocation between competitors. Because of limitations (...) of the black-box modeling there was a problem to formulate the exclusion principle correctly. Our white-box multiscale model of two-species competition is based on logical deterministic individual-based cellular automata. This approach provides an automatic deductive inference on the basis of a system of axioms, and gives a direct insight into mechanisms of the studied system. It is one of the most promising methods of artificial intelligence. We reformulate and generalize the competitive exclusion principle and explain why this formulation provides a solution of the biodiversity paradox. In addition, we propose a principle of competitive coexistence. (shrink)

Recall that for any Boolean algebra (BA) A, the cellularity of A is c(A) = sup{|X| : X is a pairwise-disjoint subset of A}. A pseudo-tree is a partially ordered set (T, ≤) such that for every t in T, the set {r ∊ T : r ≤ t} is a linear order. The pseudo-tree algebra on T, denoted Treealg(T), is the subalgebra of ℘(T) generated by the cones {r ∊ T : r ≥ t}, for t in T. We (...) characterize the cellularity of pseudo-tree algebras in terms of cardinal functions on the underlying pseudo-trees. For T a pseudo-tree, c(Treealg(T)) is the maximum of four cardinals c\sbT, ι\sbT, φ\sbT, and μ\sbT : roughly, c\sbT measures the "tallness" of the pseudo-tree T; ι\sbT the "breadth"; φ\sbT the number of "finite branchings"; and μ\sbT the number of places where T "does not branch." We give examples to demonstrate that all four of these cardinals are needed. (shrink)

We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by (...) Baldwin–Eklof–Trlifaj are stable and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický. (shrink)

Let T be an infinite pseudo-tree. In [2], we showed that the cellularity of the pseudo-tree algebra Treealg(T) was the maximum of four cardinals cT, lT, ϕT, and μT: roughly, cT is the "tallness" of T; lT is the "width" of T; ϕ is the number of "points of finite branching" in T; and μ is the number of "sections of no branching" in T. Here we ask: which inequalities among these four cardinals may be satisfied, in some sense, by (...) a pseudo-tree? We show that the possible inequalities among cT, lT, ϕT, and μT attained by pseudo-trees T are closely related to the existence of generalized Suslin trees. (shrink)

We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure M is cellular if and only if M is \-categorical and mutually algebraic. Second, if a countable structure M in a finite relational language is mutually algebraic non-cellular, we show it admits an elementary extension adding infinitely many infinite MA-connected components. Towards these results, we introduce MA-presentations of a mutually algebraic structure, in which every atomic formula (...) is mutually algebraic. This allows for an improved quantifier elimination and a decomposition of the structure into independent pieces. We also show this decomposition is largely independent of the MA-presentation chosen. (shrink)

Biomedical research is increasingly a matter of the navigation through large computerized information resources deriving from functional genomics or from the biochemistry of disease pathways. To make such navigation possible, controlled vocabularies are needed in terms of which data from different sources can be unified. One of the most influential developments in this regard is the so-called Gene Ontology, which consists of controlled vocabularies of terms used by biologists to describe cellular constituents, biological processes and molecular functions, organized into (...) hierarchies via the relation of class subsumption. Here we seek to provide a rigorous account of the logic of classification that underlies GO and similar biomedical ontologies. Drawing on Aristotle, we develop a system of axioms and definitions for the treatment of biological classes and instances. (shrink)

A complete Boolean algebra ${\mathbb{B}}$ satisfies property ${(\hbar)}$ iff each sequence x in ${\mathbb{B}}$ has a subsequence y such that the equality lim sup z n = lim sup y n holds for each subsequence z of y. This property, providing an explicit definition of the a posteriori convergence in complete Boolean algebras with the sequential topology and a characterization of sequential compactness of such spaces, is closely related to the cellularity of Boolean algebras. Here we determine the position of (...) property ${(\hbar)}$ with respect to the hierarchy of conditions of the form κ-cc. So, answering a question from Kurilić and Pavlović (Ann Pure Appl Logic 148(1–3):49–62, 2007), we show that ${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}$ is not a theorem of ZFC and that there is no cardinal ${\mathfrak{k}}$ , definable in ZFC, such that ${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}$ is a theorem of ZFC. Also, we show that the set ${\{ \kappa : {\rm each}\, \kappa{\rm -cc\, c.B.a.\, has}\, (\hbar ) \}}$ is equal to ${[0, \mathfrak{h})}$ or ${[0, {\mathfrak h}]}$ and that both values are consistent, which, with the known equality ${{\{\kappa : {\rm each\, c.B.a.\, having }\, (\hbar )\, {\rm has\, the}\, \kappa {\rm -cc } \} =[{\mathfrak s}, \infty )}}$ completes the picture. (shrink)

Protein post‐translational modifications (PTMs) play a crucial role in all cellular functions by regulating protein activity, interactions and half‐life. Despite the enormous diversity of modifications, various PTM systems show parallels in their chemical and catalytic underpinnings. Here, focussing on modifications that involve the addition of new elements to amino‐acid sidechains, I describe historical milestones and fundamental concepts that support the current understanding of PTMs. The historical survey covers selected key research programmes, including the study of protein phosphorylation as a (...) regulatory switch, protein ubiquitylation as a degradation signal and histone modifications as a functional code. The contribution of crucial techniques for studying PTMs is also discussed. The central part of the essay explores shared chemical principles and catalytic strategies observed across diverse PTM systems, together with mechanisms of substrate selection, the reversibility of PTMs by erasers and the recognition of PTMs by reader domains. Similarities in the basic chemical mechanism are highlighted and their implications are discussed. The final part is dedicated to the evolutionary trajectories of PTM systems, beginning with their possible emergence in the context of rivalry in the prokaryotic world. Together, the essay provides a unified perspective on the diverse world of major protein modifications. (shrink)

What sets someone on a life trajectory? This question is at the heart of studies of 21st-century neurosciences that build on scientific models developed over the last 150 years that attempt to link psychopathology risk and human development. Historically, this research has documented persistent effects of singular, negative life experiences on people’s subsequent development. More recently, studies have documented neuromolecular effects of early life adversity on life trajectories, resulting in models that frame lives as disproportionately affected by early negative experiences. (...) This view is dominant, despite little evidence of the stability of the presumably early-developed molecular traits and their potential effects on phenotypes. We argue that in the context of gaps in knowledge and the need for scientists to reason across molecular and phenotypic scales, as well as time spans that can extend beyond an individual’s life, specific interpretative frameworks shape the ways in which individual scientific findings are assessed. In the process, scientific reasoning oscillates between understandings of cellular homeostasis and organisms’ homeorhesis, or life trajectory. Biologist and historian François Jacob described this framework as the “attitude” that researchers bring to bear on their “objects” of study. Through an analysis of, first, historical and contemporary scientific literature and then ethnographic research with neuroscientists, we consider how early life trauma came to be associated with specific psychological and neurobiological effects grounded in understandings of life trajectories. We conclude with a consideration of the conceptual, ontological, and ethical implications of interpreting life trajectories as the result of the persistence of long-embodied biological traits, persistent life environments, or both. (shrink)

Although it has not been much noticed, reproduction is the central theme of François Jacob’s important history of biology, La logique du vivant (The Logic of Life). In a book ostensibly devoted to heredity, this molecular biologist had reproduction integrate levels of organization from organisms to molecules and play a major role in each historical transition between them, not just in the influential argument for a shift “from generation to reproduction.” Moreover, I claim, La logique was the first general (...) history of (research on) reproduction. Earlier histories had tackled only aspects of generation and reproduction; none historicized the latter. Jacob’s innovation came out of the rising prominence of reproduction in neo-Darwinist studies of populations and in his own field, the cellular genetics of bacteria and their viruses, and engagement with history and philosophy of science. The discovery of bacterial “sex” enabled microbial genetics but, ironically, led Jacob to a sexless concept of reproduction. This approach molded a history that reached across the living world but slighted sex and the complexities of reproduction in multicellular organisms. Readers can learn from its strength and limitations. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)